Shear-Thickening and Entropy-Driven Reentrance

Abstract

We discuss a generic mechanism for shear-thickening analogous to entropy-driven phase reentrance. We implement it in the context of non-relaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second and first order stirring-induced jamming transitions leading to intermittency, metastability and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a Mode-Coupling theory of shear-thickening.When liquids are subjected to strong stirring, in general their viscosity decreases, a phenomenon known as 'shear thinning'. The opposite ('shear thickening') behavior when stirring leads to increased jamming is rather exceptional and intriguing [1]. That shear-thinning should be generic is quite easy to understand by considering the structure of any system having a large viscosity and long relaxation time scales. From the point of view of the phase-space energy landscape, the long relaxation times are the consequence of directions that are either almost flat, or contain barriers that can only just be crossed. When the system is stirred by non-conservative forces, displacements are easily induced along these directions, and this has the effect of speeding the relaxation. From the real space point of view, slow relaxations are linked to extended dynamically correlated spatial regions [2], and stirring tends to break off these domains, thus making the system more fluid. It is thus no surprise that just about any system (and any model) will naturally exhibit shear-thinning.For shear-thickening instead, several explanations have been attempted, and it is at present not clear whether a universal one will apply for all possible systems. There are indications that jamming in particulate suspensions is related to increased disorder [3], and in some cases to the formation of clusters of particles in lubrication contact [4,5]. To the extent that at large densities the strongly jammed state has the appearance of an amorphous, glassy solid, shear-thickening may be thought of as a consequence of an underlying glass transition induced by stirring [6]. For such collective behavior one can attempt a theory with less focus on the details but founded on notions that are thought to be generic of glasses: this has suggested, for example, the casting of the problem in a Mode Coupling format [6].In this Letter we attempt a microscopic setting in which glassiness and shear-thickening emerge naturally and are simultaneously understood. The basic idea is to exploit the analogy between entropy-driven transitions in which systems freeze upon heating and those in which they jam under the action of stirring. To obtain concrete results, we discuss this idea within the 'Random First Order' scenario for the glass transition, although it is not restricted to it. In its simplest version, the Random First Order scenario applies to models of fully connected degrees of free...

Shear thickening in a solution undergoing inverse melting

“…Results similar to those obtained with MCT for shear thickening have been directly derived by Sellitto and Kurchan [14] starting from a spin model for inverse freezing in which a phase reentrance driven by entropy was predicted [15]. They exploited the analogy between freezing by heating and jamming by stirring to propose a mechanism for shear thickening analogous to the phase re-entrance.…”

“…On the basis of the analogy proposed by Sellitto and Kurchan [14] we interpret shear thickening in these inverse melting solutions as a driving mechanism for the glass transition, although an arrested state is not observed in the investigated shear rate and concentration range.…”

“…In this respect we could speculate that the applied shear favours the breaking of the intra-molecular hydrogen bonds (HB) of CD at a critical value 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 The connection and the similarities between the investigated inverse melting solutions and the schematic model for shear thickening and entropy driven transitions proposed by Sellitto and Kurchan [14] induces to interpret the observed shear thickening as a driving mechanism for glass transition although a transition to an arrested state is not observed in the investigated shear rate and concentration range. power-law behaviour.…”

Focused Force Transmission through an Aqueous Suspension of Granules

“…Extensional rheology studies likewise show divergences, and even brittle fracture at high strain rates [12]. The underlying mechanisms are not completely understood [13][14][15][16] but seem associated with the formation of particle clusters whose interactions cause jamming. In this study, we show that such a suspension can give rise to a focused force transmission.…”

Dynamic Jamming Point for Shear Thickening Suspensions

“…It has been suggested [3,6,7,8,9,10,11,12,13,14,15,16,17] that shear thickening is related to the phenomenon of jamming. The concept of a jamming transition, however, applies to the limit of vanishing shear rate and is exemplified by the onset of glassy behavior with a seemingly diverging viscosity in molecular liquids, dense packings of colloids, or macroscopic granular materials, leading to the appearance of a yield stress below which there is no flow [18,19,20].…”